can i publish my form to a url I own?

Yes, if you have a webpage there, you can embed your form in the page, you can check this guide to know how to get the embed codes that you have for your form and have it appear on your webpage: https://www.jotform.com/help/34-Adding-a-Form-to-a-Web-Page

If what you wish is to use your URL directly for your form as a stand alone, you may do so as well. Please check this guide on how to configure your domain to use it for URLs for your forms: https://www.jotform.com/help/144-How-to-use-Custom-Domains-with-Jotform

Feel free to let us know if you have additional questions.

Thanks.